The present paper builds upon the distributional framework that was developed to study singular solutions in linear elasticity theories in our recent work [1]}, [2]}. One of these was concerned with deriving strain compatibility and incompatibility relations for piecewise smooth linearized strain fields, possibly with concentrations over the singular interfaces [1]}, while the other dealt with equations of equilibrium and strain compatibility/incompatibility for fields with point singularities [2]}. In the latter, emphasis was placed in rigorously establishing the gap between stating the governing equations in terms of the bulk restriction of the fields (away from the singular points) and in distributional terms over the whole domain. The notion of degree of divergence was central in characterizing the gap between the two descriptions. The present work significantly deviates from these papers due to the inherently non-linear nature of the von Kármán equations. In order to pose the von Kármán equations in a distributional sense, we need to unambiguously establish the notions of a distributional determinant, a distributional inner product, and a distributional Monge-Amperè bracket, while remembering that the multiplication of two arbitrary distributions is in general not defined, see Section REF . Towards this end, we have to specify stricter regularity assumptions (including those related to the degree of divergence) on the associated fields. Overall, the present paper demonstrates a successful application of a distributional methodology to a non-linear framework with singular fields. Most importantly, it allows us to obtain local pointwise equations that hold over the singular subdomain.
